Topology and Superconductivity In and Out of Equilibrium

凝聚态物理领域涉及对材料性质的理解和控制。材料的性质是由物质的微观成分——电子和原子——决定的。微观世界是由量子力学定律支配的，而不是经典力学，它是用专门为多粒子系统（每立方厘米10^22个原子的数量级）开发的数学工具来描述的。这些工具已经存在了60多年，并且在从微观角度预测诸如导电和磁性等性质方面非常成功。特别是，朗道的费米液体理论描述了电子在有序原子晶格中的运动。在这个框架中，非常一般的论证允许物理学家对物质的状态进行分类，并研究不同状态之间的转换。******然而，由于过去十年的进步，我们现在知道一些材料与之前提出的任何类别都不匹配。更准确地说，分类应该更精细。物质的“旧”分类是基于对称的概念——系统在某些坐标变换（如时间反转、自旋旋转、点群）下的不变性，而新的分类应该包括拓扑方面以及对称方面的考虑。例如，最近发现的新材料被称为拓扑绝缘体和拓扑超导体。它们与非拓扑绝缘体和超导体的区别在于它们的拓扑结构，而不是它们的对称性。拓扑结构还具有物理后果。最值得注意的是，拓扑绝缘体在保持其表面导电状态的同时具有绝缘体积。******在发现基金的帮助下，我将继续研究物质的拓扑状态。我对使用外场驱动系统进入和退出拓扑状态特别感兴趣。特别是，人们可以施加一个时间相关的电磁场（如光）并使系统脱离热平衡。非平衡系统可能不同于非驱动系统，并且可能具有不同的拓扑性质。******我的工作是理论性的，重点是预测材料和器件的特性，并提出可行的实验。一旦可以通过施加外场来控制拓扑性质，电子学和自旋电子学领域的许多应用就会随之而来。

The field of condensed matter physics is concerned with understanding and controlling the properties of materials. Material properties are determined by the microscopic components of matter - electrons and atoms. The microscopic world is governed by the laws of quantum mechanics, rather than classical mechanics and is described mathematically with tools specifically developed for systems of many particles (of the order of 10^22 atoms per cubic cm). Such tools have existed for over 60 years and have been very successful in predicting properties like conduction and magnetism from microscopic considerations. In particular, Landau's Fermi liquid theory describes the electrons as they move through an ordered lattice of atoms. In this framework very general arguments allow physicists to classify states of matter and study transitions between different states. ******However, thanks to advances over the past decade, we now know that some materials do not match any of the previously proposed classes. To be more precise, the classification should be refined. While the 'old' classification of matter is based on the notion of symmetry - invariance of the system under some coordinate transformation (like time reversal, spin rotation, point group), the new classification should include topological aspects as well as symmetry considerations. For example, new materials which were discovered recently are called topological insulators and topological superconductors. They can be distinguished from non-topological insulators and superconductors by their topology but not by their symmetry. The topology also has physical consequences. Most notably, topological insulators have an insulating bulk while maintaining conducting states on their surfaces. .******With the help of the discovery grant I will continue to pursue the study of topological states of matter. I'm particularly interested in driving systems into and out of topological states using external fields. In particular, one can apply a time dependent electromagnetic field (like light) and drive the system out of thermal equilibrium. The non-equilibrium system may be different from the un-driven system and may posses different topological properties. ******My work is theoretical and will focus on predicting the properties of materials and devices and proposing feasible experiments. Once topological properties can be controlled by applying external fields many applications in the field of electronics and spintronics may follow.